ACIMaterialsJournal/July-August1998 365

ACI Materials Journal , V. 95, No. 4, July-August 1998.Received September 11, 1996, and reviewed under Institute publication policies.

Copyright 1998, American Concrete Institute. All rights reserved, including themaking of copies unless permission is obtained from the copyright proprietors. Perti-nent discussion will be published in the May-June 1999 ACI Materials Journal ifreceived by February 1, 1999.

ACI MATERIALS JOURNAL TECHNICAL PAPER

Freshly placed concrete exposed to hot, windy conditions is often prone to

plastic shrinkage cracking (though other conditions can also promote thisphenomenon). This type of cracking is normally noticed on slabs, pave-ments, beams, and generally other flat concrete surfaces. Many factors

affect plastic shrinkage cracking, in particular the evaporation of waterfrom the surface of freshly placed concrete. Other factors also influence thelikelihood of plastic shrinkage cracking such as water-cement ratio, fines

content, member size, admixtures, and on-site building practices. Evapora-tion itself is a function of climatic variables such as relative humidity, airtemperature, the temperature of the evaporating surface, and very impor-

tantly the wind velocity at the surface.

This paper primarily explains the background to the evaporation nomo-

graph found in ACI 305R-96, “Hot Weather Concreting” (Manual of Con-crete Practice, Part 2-1996), where the graph provides a means ofestimating the rate of evaporation of surface moisture from concrete. The

paper offers an alternative nomograph and various formulas to predict anevaporation rate of surface water (primarily bleed water) from freshlyplaced concrete surfaces. Other factors related to evaporation and plastic

shrinkage cracking are also addressed.

Keywords: air temperature; concrete temperature; cracks in concrete;durability; evaporation; high-strength concrete; hot weather concreting;humidity; plastic shrinkage; solar radiation; vapor pressure; wind.

INTRODUCTIONAnyone associated with the concrete industry and con-

fronted by hot weather problems has periodically used theACI Hot Weather Concreting evaporation nomograph1 (seeFig. 1). This graph provides a method of estimating the evap-oration rate of bleed water from the surface of freshly placedconcrete. The evaporation rate is calculated so as to givesome indication of the possible onset of plastic shrinkagecracking.

The ACI report states: “Plastic shrinkage cracking is fre-quently associated with hot weather concreting in arid cli-mates. It occurs in exposed concrete, primarily in flatwork,but also in beams and footings and may develop in other cli-mates whenever the evaporation rate is greater than the rateat which water rises to the surface of recently placed con-crete by bleeding.”

In 1992 the author began researching at a personal levelthe origin of the ACI nomograph and in particular the originof “Menzel’s formula” upon which the nomograph is based.

No references gave any clear indication of the “exact” originof the formula. By 1995 the author had finally derived Men-zel’s formula, in particular the origin of the constants in theformula, then developed a simpler set of equations and a newnomograph which can be used in lieu of Menzel’s formula orthe ACI nomograph.

RESEARCH SIGNIFICANCEPlastic shrinkage cracking is a constant source of concern

in the concrete industry. It causes anxiety between the con-crete supplier and the client when cracks (albeit hairline) areobserved on a recently placed concrete surface. It also causesconcern to the designer as “long-term durability” comes intoquestion. It is of particular concern in countries such as Aus-tralia, New Zealand, the U.S.A., South Africa, and the Mid-dle East, where hot or windy conditions are experienced(though it is not restricted only to these countries or these cli-matic conditions).

New formulas and nomographs are offered, thus assistingthe industry to more easily calculate the evaporation of waterfrom a concrete surface and accordingly predict the possibleonset of plastic shrinkage cracking. An explanation of thebackground to the ACI 305R-96 evaporation nomograph isgiven, thus helping researchers who have queried the basis ofthis graph, and in particular, its validity.

Finally, parameters such as water-cement ratio, admix-tures, depth of section, fines content, fibers, and on-sitebuilding practices are reviewed in light of research done byothers on their influence in promoting or resisting plasticshrinkage cracking.

ACI NOMOGRAPH BACKGROUNDSince 1992 the evaporation nomograph (see Fig. 1) con-

tained in the ACI Manual of Concrete Practice, Section

Title no. 95-M34

Plastic Shrinkage Cracking and EvaporationFormulas

by Paul J. Uno

ACI Materials Journal/July-August1998366

Author Bio statement appears in this box. The first paragraph in the box should usethe format BiographyLA to insert a 20 pica line abovethe box, and the last paragraphshould be assigned style BiographyLB so that a 20 pica line is niserted below the line.

305R, “Hot Weather Concreting,”1 has quoted Lerch as thereference for this chart, while prior to 1992 Bloem was quot-ed as the reference. In actual fact the nomograph was devel-oped by Bloem and produced in a July 1960 paper2 for theNational Ready Mixed Concrete Association/National Sandand Gravel Association (NRMCA/NSGA). Many of the nu-merical values upon which the nomograph was formed werepresented as a table in a paper for the Journal of the Ameri-can Concrete Institute by Lerch3 in Feb. 1957 and earlier in1955 in a Portland Cement Association (PCA) paper.4 Thedesirability to make this tabular information more easilyavailable to ready-mix concrete producers (via a graphicalmethod) was suggested to Bloem prior to 1960 by J. MontyHoward, engineer for the Dolese Company of OklahomaCity.

This evaporation table, however, was first published byCarl A. Menzel,5 as outlined in a paper he wrote in 1954 forthe PCA. The values in the table and those required to pro-duce the Bloem nomograph were derived using Menzel’sformula, which is shown below as Eq. (1)

(1)

whereW = weight (lb) of water evaporated per square foot of sur-face per hour (lb/ft2/hr),eo = pressure of saturated vapor pressure at the tempera-ture of the evaporating surface, psi,

ea = vapor pressure of air, psi, and

V = average horizontal air or wind speed measured at alevel about 20 in. higher than the evaporating surface, mph.

The ACI nomograph is still the preferred method for pre-dicting the evaporation rate of bleed water from the surfaceof freshly placed concrete due to the difficulty in using Men-zel’s equation. The Menzel formula requires the input of va-por pressure of air and the pressure of saturated vapor overthe water surface of the concrete—both conditions being dif-ficult to measure on site. It is interesting to note that in Men-zel’s original paper he also presented an evaporationnomograph but it required the values of dewpoint to establishvapor pressures—again difficult parameters to measure orobtain generally. As mentioned in the introduction, the ori-gin of Menzel’s formula, in particular the derivation of theconstants in his formula, has not been apparent to many in-volved in concrete research and development.6,7

ORIGIN OF MENZEL’S FORMULAMany researchers have questioned the applicability of

Menzel’s formula under particular weather conditions, but asMather8 states, “The formula is valid regardless of whetherthe water surface from which the evaporation is taking placeis a lake, pond, reservoir, pan, the bleed water layer over a

W 0.44 eo ea–( ) 0.253 0.096V+( )=

slab of fresh concrete, or the layer of water over a hardenedconcrete surface covered by water.”

Menzel did not invent his formula since formulas of thistype are merely adaptations of the standard form of evapora-tion formula outlined by Dalton9 in 1802, namely

(2)

where E = evaporation rate,(eo – ea) = pressure difference, andf(u)= wind function.

While Dalton did not produce the standard formula above,he provided the scientific principles upon which this type offormula was based. However, if one refers to the many hun-dreds of books and papers written on evaporation and hy-drology since that period, one will find many equations forpredicting evaporation. So how did Menzel arrive at his for-mula?

In December 1948 various U.S. government bodies, in-cluding the Weather Bureau, decided to undertake researchtesting in the area of water loss from reservoirs. They ulti-mately carried out extensive water loss investigations atLake Hefner between 1950 and 195210,11 measuring air tem-peratures, humidities, wind velocities, solar radiation, pre-cipitation, pan evaporations, and pan water temperatures(using various pan types and sizes). One of the objectives of

E eo ea–( )f u( )=

ACI member Paul J. Uno is the State Engineer—Structural and Building, New SouthWales, for the Cement and Concrete Association of Australia, Sydney Office. He hasgained over 20 years experience in structural design and civil engineering construc-tion in Australia. He has also written papers on the acoustic and thermal advantagesof concrete.

Fig. 1—ACI nomograph for estimating rate of evaporation of surface moisture from concrete1

ACI Materials Journal / July-August 1998 367

these tests was to establish better correlations between panevaporation and lake evaporation. It is from these LakeHefner tests that Menzel derived his well-known formula.

The Lake Hefner tests were one of the most comprehen-sive series of water loss tests carried out up to this period(prior comprehensive tests of evaporation from free watersurfaces were carried out by Rohwer12 in 1931) and thesetests carried out by researchers such as Kohler, Harbeck, andothers produced many evaporation equations. One of themain evaporation formulas which developed from the LakeHefner tests carried out by Kohler in the 1950 to 1952 period(and quoted in most hydrology texts to this date on this sub-ject) is shown as Eq. (3) below

(3)

where E = evaporation rate, in./day,u = wind velocity, miles/day, and(eo – ea) = pressure difference, in. Hg.

This was not the equation that Menzel used as this equa-tion was based on the evaporation rates derived from theStandard Class A pan tests. These pans were 4 ft (122 cm) indiameter and 10 in. (25 cm) deep and supported on a woodframe above ground level. The test results from which Men-zel derived his constants in Eq. (1) came from the LakeHefner tests where the BPI (Bureau of Plant Industry) sunk-en pans had been used since these pans were of larger diam-eter (6 ft or 183 cm) and deeper (2 ft or 61 cm) than theStandard Class A pans and as such provided a better index.In fact the Lake Hefner report stated, “The physical charac-teristics of the BPI (sunken) pan seem to be most nearly rep-resentative of those of a natural body of water and thereforethis pan merits high consideration on a theoretical basis.”

Two standard forms of evaporation formula were quotedin the Lake Hefner report as “both being suitable for use”[see Eq. (4) and (5)]. The report stated, “Although these twoequations appear almost quite different they fit observed dataalmost equally well because of the limited range of wind da-ta.” The two equations are shown below where a, b, c, and nare constants derived from tests and u is the wind velocity.

(4)

or

(5)

The constants a and b in Eq. (4) were determined byKohler as 0.253 and 0.0040, respectively, with a correlationindex of 0.91. Since u was in miles per day the conversion tomph meant the constant b now became 0.096. The pressuredifference units were in inches of mercury (in. Hg) and sowere converted to psi; similarly, E was in in./day and had tobe converted to lb water/ft2/hr. These two last conversionsresulted in a 0.44 factor being required at the beginning of

the formula. The Menzel equation for evaporation [shownearlier as Eq. (1)] finally became

E = 0.44 (eo – ea) (0.253 + 0.096V)

It can thus be seen that the formula quoted for many yearsas Menzel’s formula was really an adaptation of Kohler’sformula. Whichever formula is used, they all require themeasurement of vapor pressures. As mentioned earlier, theBloem nomograph resolved this problem in 1960 by usingrelative humidity and concrete water temperature as equiva-lent variables based upon standard psychrometric data (thus,the need for vapor pressures had been eliminated).

NEW AND EASIER FORMULASSince the onset of calculators and computers the need for

graphical systems has generally waned in favor of equations(albeit that the equations might be more complicated). Thishas resulted in attention being focussed back to Menzel’sequation. As mentioned earlier the problem with his equa-tion was the vapor pressure difference requirement. Manyhave developed equations which relate vapor pressure to rel-ative humidity and temperature but most of these equationswhile very accurate are somewhat long and complicated.13,14

An easier and yet still very accurate equation which relatestemperature and vapor pressure is one developed by Tetens15

in 1930 as referenced by Murray,16 Dilley,17 and Mills.18 Ithas been shown that Eq. (6) and (7) are accurate to within0.001 percent for the temperature range 50 to 104 F (10 to40 C). This equation (the metric form) is used by the WorldMeteorological Organization at the present.

In.-lb units

(6)

where es = saturation vapor pressure, psi, andT = temperature, F.

Metric units

(7)

where es = saturation vapor pressure, kPa, andT = temperature, C.

By merely substituting the air temperature and concrete(water) temperature into Eq. (6) or (7), one obtains the re-spective vapor pressures for air and the concrete water sur-face. These vapor pressures are then substituted into themodified version of Menzel’s equation shown below

In.-lb units

(8)

E eo ea–( )0.88 0.37 0.0041u+( )=

E eo ea–( ) a b u+( )=

E c eo ea–( )un=

es 0.0885 17.3 T 3 2–( )T 395.1+( )

-------------------------------exp=

es 0.61 17.3T237.3 T+( )

----------------------------exp=

E 0.44 e so r.esa–( ) 0.253 0.096V+( )=

ACI Materials Journal / July-August 1998368

where E = evaporation rate, lb/ft2/hreso= vapor pressure at concrete surface (psi) from Eq. (6)esa= vapor pressure of air (psi) from Eq. (6)r = (RH percent)/100V = wind velocity, mph

Metric units

(9)

whereE = evaporation rate, kg/m2/hreso = vapor pressure at concrete surface (kPa) from Eq. (7)esa = vapor pressure of air (kPa) from Eq. (7)r = (RH, percent)/100V = wind velocity, kph

Example 1Air temperature Ta = 80 F (26.7 C)Conc. temperature Tc = 85 F (29.4 C)Relative humidity RH = 50 percentWind velocity V = 20 mph (32 kph)

givesAir vapor pressure esa6 (esa7) = 0.508 psi (3.51 kPa)Conc. vapor pressure eso6 (eso7)= 0.598 psi (4.11 kPa)

thusEvaporation rate E8 (E9) = 0.329 lb/ft2/hr (1.60 kg/m2/hr)Evaporation rate Eaci nomo =0.33 lb/ft2/hr (1.6 kg/m2/hr)

The author has developed a “single operation” equation(based upon Menzel’s formula) which can be used on a sim-ple hand-held calculator and which does not require vaporpressure precalculations. This is possible since a tempera-ture-vapor pressure relationship, with a correlation coeffi-cient of 0.99 for the temperature range 15 to 35 C (59 to 95F), has already been incorporated into the equation. This for-mula is very appropriate for on-site quick checks to see ifevaporation is going to be a critical factor in plastic shrink-age cracking. These simpler formulas are shown below asEq. (10) and (11)

In.-lb units

(10)

whereE = evaporation rate, lb/ft2/hr,Tc = concrete (water surface) temperature, F,Ta = air temperature, F,r = (RH percent)/100, andV = wind velocity, mph.

Metric units

(11)

where

E = evaporation rate, kg/m2/hr,Tc = concrete (water surface) temperature, C,Ta = air temperature, C,r = (RH percent)/100, andV = wind velocity, kph.

Using Example 1 again, the evaporation rates using Eq.(10) and (11) yield 0.342 lb/ft2/hr and 1.67 kg/m2/hr, respec-tively.

Table 1 shows a summary of the evaporation rates usingall these formulas and compares them to Menzel’s rates. Ascan be seen from the table, the calculated evaporation ratesusing the new formulas, i.e., Eq. (8) to (11), come very closein most cases to those rates derived using Menzel’s equationand shown in the 1955 PCA publication and corresponding1957 Lerch table.

The author has also produced a simpler nomograph forquickly estimating evaporation based upon the situationwhere the concrete temperature and the air temperature arethe same (see Fig. 2)—an assumption that is often madewhen concrete temperatures are not available. If, however, amarked difference between air and concrete temperaturedoes exist, then the ACI nomograph or the equations listed inthis paper should be used.

ENVIRONMENTAL FACTORSAs can be seen from the formulas the environmental fac-

tors that play a key role in evaporation are wind, air temper-ature, humidity, and water surface temperature. One factorthat seems to have been overlooked when analyzing theseformulas is solar radiation. It too plays a key role in the evap-oration and plastic shrinkage cracking process and is ac-counted for in these formulas (as will be explained later). Letus address each of these environmental factors individually.

EvaporationThis is the process by which a liquid is converted into a va-

por or gas. This can happen where: a) heat energy is ab-sorbed into the liquid, e.g. by solar radiation; or b) where thepressure above the liquid surface is less than that in the liq-uid, thus allowing the active water molecules to escape fromthe liquid as vapor.

This evaporation process is then accelerated if wind ispresent to continually remove escaping water molecules.The loss in energy from the evaporating water surface meansthat the temperature of the surface water decreases, therebyslowing down further evaporation.

WindWind is one of the most important considerations in con-

trolling plastic shrinkage cracking. It can be measured or es-timated in many ways, e.g., using anemometers, ventimeters,wind socks, and even observations of the surrounding ele-ments. For precision, pressure tube anemometers or four andthree cup anemometers can be used; however, if approxi-mate wind speeds will suffice, then the Beaufort scale19 canbe adopted (see Table 2). This scale, first devised by AdmiralSir Francis Beaufort in 1805, has been used for many yearsto predict wind speed by making use of the movement of sur-rounding elements, e.g. trees, smoke, or waves. One problem

E 0.313 e so r e sa⋅–( ) 0.253 0.06V+( )=

E Tc2.5

r.Ta2.5

–( ) 1 0.4V+( )6–

×1 0=

E 5 Tc 18+[ ]2.5 r Ta 1 8+[ ]2.5⋅–( ) V 4+( ) 6–×1 0=

ACI Materials Journal / July-August 1998 369

with using predetermined wind speed values is ascertainingthe level at which the wind speeds were measured (sincewind varies exponentially with height).

When the Lake Hefner tests were conducted using BPIpans, the top rim of these pans was located approximately 2in. (50 mm) above the ground surface level. The anemome-ters used (three cup) for these same tests were mounted 6 in.(150 mm) above the rim of the Class A pans in the same testarea. These Class A pans were 10 in. (250 mm) deep andmounted on a standard wooden platform such that the bot-tom of the Class A pan was 6 in. (150 mm) above the groundsurface. From these values it can be seen that the anemome-ters recording the wind speeds for the Lake Hefner tests werelocated 20 in. (500 mm) above the top rim of the BPI pans.This is the height which Menzel quotes in his paper as beingthe height at which speeds should be recorded when usinghis equation stating “horizontal air or wind speed, ..., should

be measured at a level about 20 in. higher than the evaporat-ing surface.”

Unfortunately, the ACI nomograph does not highlight thisrequirement for wind measurement and so appreciable errorin calculated evaporation rates can be introduced if wind val-ues are used based upon measurements taken at higher lev-els, e.g., Weather Bureau readings (taken at a height of 10 m[33 ft] in many countries). If, however, hand-held anemom-eters are used to determine wind speeds on site, then the dif-ference should be negligible.

Kohler, in his book Engineering Hydrology,20 quotes twoformulas which address this issue. The more precise formulafor converting wind speeds at different heights and from dif-ferent surfaces is shown as Eq. (12). A simpler but slightlyless accurate formula for converting wind speeds in the layerrange 0 to 10 m (33 ft) is Eq. (13). These two models thusconvert horizontal wind velocity at a datum level to wind ve-locity at a new height

Table 1—Comparisons of evaporated rates (based on the Menzel/Lerch format)

Group Condition Case

Concrete temperature,

C (F)

Airtemperature,

C (F)

Relativehumidity,percent

Windspeed,

kph (mph)

EvaporationEq. (1) Menzel,

kg/m2/hr(lb/ft 2/hr)

EvaporationEq. (9) [Eq. (8)]

Uno,

kg/m2 /hr(lb/ft2 /hr)

EvaporationEq. (11) [Eq. (10)]

Uno,

kg/m2/hr(lb/ft2/hr)

1Increase

windspeed

1

21 (70) 21 (70) 70

0 (0) 0.07 (0.015) 0.06 (0.012) 0.06 (0.012)

2 8 (5) 0.19 (0.038) 0.17 (0.035) 0.17 (0.036)

3 16 (10) 0.30 (0.062) 0.28 (0.058) 0.28 (0.061)

4 24 (15) 0.42 (0.085) 0.40 (0.081) 0.40 (0.086)

5 32 (20) 0.54 (0.110) 0.51 (0.104) 0.51 (0.110)

6 40 (25) 0.66 (0.135) 0.62 (0.127) 0.63 (0.135)

2Decreaserelative

humidity

7

21 (70) 21 (70)

90

16 (10)

0.10 (0.020) 0.09 (0.019) 0.09 (0.20)

8 70 0.30 (0.062) 0.28 (0.058) 0.28 (0.061)

9 50 0.49 (0.100) 0.47 (0.097) 0.47 (0.102)

10 30 0.66 (0.135) 0.66 (0.135) 0.66 (0.143)

11 10 0.86 (0.175) 0.85 (0.174) 0.85 (0.184)

3

Increaseconcrete

temperatureand air

temperature

12 10 (50) 10 (50)

70 16 (10)

0.13 (0.026) 0.14 (0.028) 0.12 (0.026)

13 16 (60) 16 (60) 0.21 (0.043) 0.21 (0.041) 0.20 (0.041)

14 21 (70) 21 (70) 0.30 (0.062) 0.28 (0.058) 0.28 (0.061)

15 27 (80) 27 (80) 0.38 (0.077) 0.41 (0.081) 0.41 (0.085)

16 32 (90) 32 (90) 0.54 (0.110) 0.54 (0.112) 0.53 (0.115)

17 38 (100) 38 (100) 0.88 (0.180) 0.76 (0.152) 0.70 (0.150)

4Decrease

airtemperature

18

21 (70)

27 (80)

70 16 (10)

0.00 (0.000) 0.00 (0.004) 0.00 (0.004)

19 21 (70) 0.30 (0.062) 0.28 (0.058) 0.28 (0.061)

20 10 (50) 0.60 (0.125) 0.62 (0.127) 0.66 (0.143)

21 –1 (30) 0.81 (0.165) 0.79 (0.163) 0.87 (0.187)

5Cold airhigh RHand wind

22 27 (80)

4 (40) 100 16 (10)

1.00 (0.205) 1.05 (0.206) 1.13 (0.235)

23 21 (70) 0.63 (0.130) 0.64 (0.129) 0.72 (0.154)

24 16 (60) 0.35 (0.075) 0.38 (0.072) 0.45 (0.088)

6 Cold air andvariable wind

25

21 (70) 4 (40) 50

0 (0) 0.17 (0.035) 0.16 (0.033) 0.17 (0.035)

26 16 (10) 0.79 (0.162) 0.79 (0.161) 0.84 (0.179)

27 40 (25) 1.75 (0.357) 1.73 (0.353) 1.84 (0.395)

7Averageweather

conditions

28 27 (80)

21 (70) 50 16 (10)

0.86 (0.175) 0.88 (0.174) 0.88 (0.183)

29 21 (70) 0.49 (0.100) 0.47 (0.097) 0.47 (0.102)

30 16 (60) 0.22 (0.045) 0.22 (0.039) 0.20 (0.036)

8

High concreteand air

temperature + low RH

31

32 (90) 32 (90) 10

0 0.34 (0.070) 0.34 (0.070) 0.32 (0.069)

32 16 (10) 1.64 (0.336) 1.63 (0.336) 1.60 (0.345)

33 40 (25) 3.58 (0.740) 3.56 (0.735) 3.50 (0.760)

ACI Materials Journal / July-August 1998370

(12)

or

(13)

where V = resultant wind velocity at the new height requiredVx = wind velocity at the height measuredz = new height requiredzo = roughness lengthz1 = standard heightk = constant

If we use the better wind model as shown by Eq.(12)where zo is taken as 0.001 cm (open water), z is 0.5 m (20in.), and z1 is 10 m (33 ft), this latter value being a standardheight used by many Weather Bureaus around the world, wearrive at an equivalent wind velocity of 68 percent of thestandard wind velocity at 10 m (33 ft).

If we use the approximate wind model shown by Eq. (13)where the standard value for the constant k is taken as 1/7,and z1 is again 20 in. (0.5 m), the equivalent wind velocitywe achieve this time is 65 percent of the standard wind ve-locity at 10 m (33 ft). It can thus be seen that a reasonable ap-proximation for wind velocities to be used with Menzel’sformula, the ACI nomograph or the author’s equations, isrepresented by the simple expression shown as Eq. (14)

(14)

where

VVX

------

zz0

---- 1+ ln

z1

z0

---- 1+ l n

-------------------------=

V VXzz0

---- k

×=

Ve 2 3⁄ V std( )=

Fig. 2—Evaporation rates when air and concrete temperature are the same: (a) relative humidity; (b) air temperature vs. wind speed

(a)

(b)

ACI Materials Journal / July-August 1998 371

Ve = equivalent wind velocity at 20 in. (0.5 m)Vstd = wind velocity at the standard height of 10 m (33 ft)

When using Beaufort tables it is important to note that thewind speeds shown are at the standard height of 10 m (33 ft)above open flat ground.19 The author has included an extracolumn (equivalent wind speeds) in the standard Beaufort ta-ble (see Table 2) based on Eq.(14) for use with the evapora-tion prediction methods nominated in this paper.

Air temperatureMeasurement of this variable is quite straightforward and

basically no different to the standard way in which most peo-ple would measure air temperature, the only provision beingto measure away from the direct rays of the sun (thus mini-mizing the direct solar radiation component).

Air temperatures for the Lake Hefner tests were based onmean three hourly readings then averaged for the day. In allcases the measurements were recorded without direct sun onthe air temperature instrumentation.

Relative humidityRelative humidity is the ratio of the actual amount of mois-

ture (lb/ft3 or kg/m3) present in a unit volume of air to theamount of moisture (lb/ft3 or kg/m3) the air could hold (sat-uration) at a particular temperature—normally expressed asa percentage. When relative humidity reaches 100 percent,evaporation normally ceases unless other forces (e.g. wind)replace the saturated air with nonsaturated air.

Relative humidity readings can be obtained by contactingthe Weather Bureau or they can be recorded on site by meansof a hand-held sling psychrometer or even a simple wet bulb/dry bulb thermometer.

Concrete (water) temperatureAs explained earlier, it is really the temperature of the

bleed (or surface) water that needs to be measured to estab-lish the vapor pressure difference between the air and water

surface. Since it is difficult to measure the bleed water tem-perature, the concrete temperature is assumed to be at thesame temperature as the bleed water above and so it is theconcrete temperature that is measured. It would be difficult,however, to accurately assign a temperature component fromany heat of hydration in the first few hours after placement.

Solar radiationSolar radiation affects overlying air and land mass temper-

atures. It takes only 2.5 kJ (540 cal) of energy to convert onegm (1/28 oz) of water from a liquid to a vapor and consideringbetween 16 and 24 MJ of energy falls on each square meterof land mass in Australia on an average summer day (21 to33 MJ, i.e., 20 to 31 thousand BTUs in the U.S.A.); evapora-tion (and subsequent precipitation) is a major function of so-lar radiation.

Although the ACI nomograph does not include solar radi-ation as a variable it is accounted for in Menzel’s equationsince the Lake Hefner pans were exposed to direct and dif-fuse solar radiation for both clear and cloudy days during thetwo years of measurement. The solar contribution to evapo-ration was quantified by Kohler and others but required themeasurement of solar radiation on site, e.g., by use of apyrheliometer.

While many evaporation formulas have been quoted21

over the past 100 years, they mainly fell into one of two ap-proaches, those that were based upon “energy budget” prin-ciples (i.e., the inflow and outflow of energy which theninfluences the vaporization of water), and those that werewas based upon “aerodynamic” principles as outlined in thispaper so far. The energy budget method takes into accountthe net radiation absorbed by the water and energy increasestored in the water, the latent heat of vaporization, and the ra-tio of heat loss by conduction to heat loss by evaporation (theBowen Ratio). In 1948 Penman22 successfully combinedthese two approaches to produce his well-known “combina-tion” formula [Eq.(15)], namely

* Equivalent wind speeds [as per Eq. (14)] to be used in evaporation equations

Table 2—Modified Beaufort wind speed guide

Beaufort no. DescriptionWind speed,

knots

Wind speedVstd at 30 ft,

mph

Equivalent wind speed Ve at 20 in.,

mph*

Wind speedVstd at 10 m,

kph

Equivalent wind speed Ve at 0.5 m,

kph* On landWave height sea observed from coast, in. or ft (m)

0 Calm < 1 < 1 < 1 < 1 < 1 Calm; smoke rises vertically Sea like mirror, 0 in. (0)

1 Light air 1-3 1-3 1-2 1-5 1-3Wind direction shown by smoke drift but not wind

vanes

Ripples with the appearance of scales, 4 in. (0.1)

2 Light breeze 4-6 4-7 3-4 6-11 4-7Wind felt on face; leaves

rustle; ordinary vanes moved by wind

Small wavelets; crests do not break, 8 in. (0.2)

3 Gentle breeze

7-10 8-12 5-8 12-19 8-12Leaves and small twigs in

constant motion; wind extends light flag

Large wavelets; crests begin to break, 2 ft (0.6)

4 Moderate breeze

11-16 13-18 9-12 20-28 13-18 Raises dust and loose paper; small branches are moved

Small waves become longer, 3 ft (1)

5 Fresh breeze 17-21 19-24 13-16 29-38 19-25Small trees in leaf begin to

sway; crested wavelets form on inland waters

Many white horses formed,6 ft (2)

6Strong breeze 22-27 25-31 17-20 39-49 26-32

Large branches in motion; whistling heard in telegraph wires; umbrellas hard to use

Large waves, 10 ft. (3)

ACI Materials Journal / July-August 1998372

(15)

whereE = total evaporation,∆ = slope of the saturation curve,

,

γ = pschrometric constant,= 0.066 kPa/C,

Qn = solar radiation (see Ref. 20 for formula), andEa = evaporation from aerodynamic formulas.

While this equation has the advantage of quantifying thecontribution to evaporation by aerodynamic effects and solarradiation respectively, one drawback it has (besides havingto record accurate radiation values) is that it is based on thepremise that the water temperature and the air temperatureare the same. This assumption, as Kohler states, “can resultin an appreciable overestimation of evaporation under calm,humid conditions and a corresponding underestimate for dry,windy conditions.”

The question remains, “Does the water evaporate faster orslower when exposed to direct ‘clear sky’ (i.e., more intense)radiation as opposed to diffuse ‘cloudy sky’ (i.e., less in-tense) radiation and does it hinder or help plastic shrinkagecracking?” Various researchers have expressed differingpoints of view in this area. Research by Hasanain et al.23 in-dicated that shading concrete from direct, intense sun can re-duce evaporation by as much as 50 percent. Tests on cementmortars by Ravina and Shalon24 showed evaporation to begreatest when the samples were exposed to radiation. VanDijk and Boardman25 indicate that while radiation raises thetemperature of the surface of the concrete and the rate ofevaporation, it also induces accelerated hydration of the ce-ment and thus strengthens the concrete surface. Due to thisphenomenon, they indicate that slabs cast in the shade some-times exhibit more cracking than slabs cast in the sun.

Having commented on the environmental factors whichcause evaporation of bleed water, let us now address thebleeding rate of fresh concrete.

BLEEDING RATEThe ACI report states that “precautions should be taken

when the rate of evaporation is expected to approach 0.2 lb/ft2/hr(1.0 kg/m2/hr).” The Canadian Code26 nominates 0.75 kg/m2/hras the critical value while Australian references27 quote0.5 kg/m2/hr as a value at which precautions should be takenand a value of 1.0 kg/m2/hr as that value where plasticshrinkage cracking is likely to occur. The 0.2 lb/ft2/hr ACIfigure first appeared in the July 1960 NRMCA article.2 It ap-peared again in Modern Concrete (Oct. 1960) referenced asTechnical Information Letter No. 171 for the NRMCA.28

Both stated, “Data in literature suggest that concrete bleedrates for usual conditions of slab construction will lie in therange of about 0.1 to 0.3 lb/ft2/hr. Thus, when evaporationrate exceeds the lower of these figures, trouble with plasticcracking is potentially in the making. Conditions producing

evaporation of as much as 0.2 to 0.3 lb per sq ft per hourmake the institution of precautionary measures almost man-datory.” It is interesting to note that this evaporation rangeand the corresponding evaporation chart were not present ina 1967 version of the ACI “Hot Weather Concreting” report.

The author can only assume that since the value of 0.2 lb/ft2/hr (1.0 kg/m2/hr) first quoted in 1960 was based upon“data in literature ...” and that one of the most thorough re-search programs producing data which addressed concretebleeding was carried out by Powers29 in 1939 at the PortlandCement Association, that it is from this latter source that the0.2 lb/ft2/hr figure first originated.

Work by Powers resulted in bleeding rates in the range of32 × 10-6 to 113 × 10-6 cm/sec which equates to 0.24 to 0.83lb/ft2/hr (1.15 to 4.1 kg/m2/hr). It is thus more than likely thata lower bound figure of approximately 0.2 was adopted asthis bleed rate would be the most critical for high evapora-tion conditions. In his 1968 publication Properties of Con-crete ,30 Powers included the Menzel/Lerch evaporation tableand stated, “Bleeding among different mixes made with thesame materials may range from 20 × 10-6 to 100 × 10-6 cm/secdepending upon the cement content. In all cases the period ofconstant rate lasts 15 to 30 minutes at the most and thereafterthe rate diminishes, reaching zero within an hour and a half.Thus we see that there are very few atmospheric conditionsunder which the rate of evaporation may not exceed the rateof bleeding before which settlement is completed.” The20 × 10 -6 cm/sec rate he nominated converts to 0.15lb/ft2/hror 0.72 kg/m2/hr—similar to the Canadian limit.

PLASTIC SHRINKAGE CRACKINGIn 1942 Swayse31 defined plastic shrinkage as “a volumet-

ric contraction of cement paste (the magnitude of this con-traction being of the order of 1 percent of the absolute

volume of the dry cement)” whereas today the ACI definesit as “shrinkage that takes place before cement paste, mortar,grout, or concrete sets.” Plastic shrinkage cracking is thusthe cracking that develops primarily in the top surface of thefreshly laid (plastic) concrete due to this volumetric contrac-tion of the cement paste which is accelerated by loss of sur-face bleed water via evaporation.

Freshly placed concrete sometimes does not have suffi-cient time to develop enough tensile strength to resist con-traction stresses induced in capillary pores32 by rapidevaporation; thus cracks can develop throughout the top sur-

face of the concrete. These cracks are normally parallel andonly in the surface of the concrete; however, there can becases where they extend totally through the slab (aggravatedby drying shrinkage) and can also be random in appearance.It is interesting to note, however, that research by Ravina andShalon24 in 1968 did indicate that cracking can still occureven when evaporation is negligible (in particular when ther-mal strain exceeds concrete strain capacity).

There are a whole range of other factors which influenceplastic shrinkage cracking (other than evaporation rate). Wewill now address each of these in turn.

EQn .∆ γ.Ea+

∆ γ+( )-----------------------------

=

4098.es

237.3 T+( )2------------------------------=

ACIMaterialsJournal/ July-August1998 373

OTHER FACTORS INFLUENCING PLASTIC SHRINKAGE CRACKING

Factors relating to the properties of the fresh concrete, on-site concrete practices, and other variables which have an in-fluence on plastic shrinkage cracking have been listed belowand are subsequently addressed individually. They include

a) concrete strength (related to the total cement or bindercontent)

b) depth of concrete section (related to the bleeding capac-ity)

c) fines content (related to water demand)d) plastic state of the mix (i.e., semi-plastic, plastic, wet)e) admixtures (primarily retarders)f) fibers (primarily nylon or polypropylene)g) sub-base preparation (primarily sub-base membranes)h) surface sprays (primarily aliphatic alcohols)

Concrete strengthUse of the ACI “single value” critical evaporation rate has

been questioned by many researchers over the years. Recentresearch by Samman, Mirza, and Wafa33 highlight the prob-lems associated with only using the 0.2 lb/ft2/hr (1.0 kg/m2/hr)evaporation rate. Their research showed that high-strengthconcrete mixes containing high proportions of cement (withand without silica fume) produced concretes with low bleedrates and subsequently high susceptibility to plastic shrink-age cracking. Other research34 of a similar nature has beenperformed with cement mortars, though cement mortarswould be more prone to plastic shrinkage cracking than con-cretes due to the greater paste content per unit volume.

The author has plotted the results of the Samman et al.tests in a different form to that originally illustrated in theirpaper by comparing concrete strength, evaporation rate, andcrack area all in the one diagram (see Fig. 3). A straight linewas produced to approximate the commencement of surfacecracking for the various strengths of concrete with Eq. (16)and (17), providing a means of relating concrete strength andevaporation for the Samman tests.

Metric units

(16)

where Emax = max allowable evaporation rate, kg/m2/hr, andfc = strength of concrete, MPa.

In.-lb units

(17)

where Emax = max allowable evaporation rate, lb/ft2/hr, andfc = strength of concrete, psi.

While Eq.(16) and (17) are based only on the few tests car-ried out by Samman et al., the author believes an equation ofthis form addressing the concrete strength (or w/c ratio) ver-sus evaporation relationship should be present in the ACIrecommendations rather than the “single figure” approach.

Emax 1.6 0.016 f c–=

Emax 0.33 22.66–

×10 f c–=

Depth of sectionThe depth of section determines the bleed capacity of the

concrete since a deeper section will contain more solids tosettle and correspondingly more bleed water to rise to thesurface (see Van Dijk25). Research by Schiessl andSchmidt35 in 1990 demonstrated the linear relationship be-tween total bleeding capacity and the bleeding rate.

This depth factor more often has an effect on plastic “set-tlement” cracking (i.e., cracks formed over reinforcement orlarge aggregate); however, in light of the ability of a deepersection to produce bleed water supply to the concrete surfaceover a longer period, this should tend to resist the prematureonset of cracks. Kral and Gebauer36 found the critical evap-oration period was between two and 41/2 hr after castingwhen combined with high winds (not the first hour or two asusually thought). This would imply that deeper sectionsshould be less prone to plastic shrinkage cracking (however,more prone to plastic settlement cracking).

Fines contentThe high proportions of fine aggregate, special cements

(e.g, low heat cements), or fine supplementary cementiousmaterials (e.g. fly ash, slag, and silica fume) in some con-cretes would tend to reduce the bleed rate of concretes bymere fact of the greater surface area presented to the mixingwater volume. Add to this the fact that these materials do notcontribute significant strength gain in the very short termwould imply that these concretes should warrant special pre-cautions at lower rates of evaporation.

Plastic stateThe research by Ravina and Shalon24 mentioned earlier on

cement mortar samples also concluded that plastic shrinkagecracking was worst for the wet and plastic mortars (where w/cratios were 0.7 and 0.5 respectively) yet least for the semi-plastic mortars (w/c ratio of 0.6). This differs, however, fromthe findings of Wittman32 where the critical plastic state formaximum cracking was nominated at a w/c ratio of 0.52 withlower or higher w/c ratios being less prone to plastic shrink-age cracking. Tests on 104 concrete samples by Kral andGebauer36 confirmed that extremely dry or extremely fluidmixes were less susceptible to shrinkage cracking.

Fig. 3—Concrete strength and evaporation rate compared with crack area (adapted from Ref. 33) (“•” indicates zero plastic shrinkage crack area; “x” indicates crack areas in mm2 shown above dotted lines)

ACI Materials Journal / July-August 1998374

AdmixturesThe concretes of today, while not that unlike those in the

40s and 50s, do on many occasions have a variety of admix-tures introduced into the mix which have an influence onplastic shrinkage cracking. The use of water-reducing agents(water reducers), high-range water-reducing agents (super-plasticizers), accelerating and retarding agents (acceleratorsand retarders), and oxides all affect the plastic state of theconcrete in some manner. Research by Cabrera37 indicatesthat concretes containing superplasticizers, while bleedingless, tend to resist or prolong the onset of plastic shrinkagecracking due to the modification in concrete surface tension.Research generally has shown that excess use of retardingadmixtures can make freshly placed concrete more suscepti-ble to plastic shrinkage cracking due to the slower set andstrength gain of the mix.38 In relation to water-reducing ad-mixtures, oxides, and accelerating admixtures, the use of awater-reducing admixture would affect the plastic state ofthe concrete and so would have to be addressed as per thecomments in the section on plastic state; oxides relate to thefines content of a mix and so the section on Fines concretewould apply; while accelerators hasten set and so should de-crease the likelihood of cracking.

FibersThe use of fibers in concrete over the past few years has

resulted in much research39,40 being carried out in this area,in particular with polypropylene fibers. The general consen-sus is that polypropylene fibers do provide some improve-ment to reducing the onset of plastic shrinkage cracking byholding or stitching the plastic concrete surface together,thus minimizing the formation of early microcracks. Onepoint to note is that the introduction of fibers can reduce thebleed rate of the concrete via the increased fiber surface areaintroduced into the mix. This can in some cases result in con-crete placers adding more water to the mix to make it moreworkable, thereby reducing the concrete strength accordingly.

Sub-base preparationThe sub-base materials under a concrete slab have also

been shown to have a definite effect on plastic shrinkagecracking (and longer term drying shrinkage cracking). Testscarried out by Campbell et al.41 using three sub-base condi-tions, plastic sheeting (polyethylene), sand, and sand-cementmix respectively, showed that extensive cracking only devel-oped on exterior concrete slabs with plastic sheeting under-neath; however, Turton42 disputes this phenomenon basedupon his observations in the U.K.

Surface spraysTests carried out in the U.S. by Koberg and others43 be-

tween 1959 and 1960 looked at the suppression of evapora-tion control from lakes and reservoirs by the use ofmonomolecular films (alkanols). This research stemmedfrom earlier tests done in Australia in 1952 by Mansfieldwhere field testing of monolayers reported evaporation re-ductions in the order of 30 percent. Subsequent testing donein 1965 at Utah University44 confirmed that evaporation ofbleed water could also be suppressed by the application of

aliphatic alcohols with reductions in evaporation of 75 per-cent achieved.

To summarize the standard precautions for minimizing theonset of plastic shrinkage cracking:

a) Use wind breaks to reduce the air flow over the top sur-face of the concrete.

b) Use evaporative retarders such as aliphatic alcohols.c) Consider the use of fibers.d) Address the fines content in the mix.e) Avoid admixtures that reduce bleed rate (without some

improved surface tension).f) Avoid the excess use of retarders.g) Determine if plastic membranes under slabs are re-

quired (e.g., to stop rising damp).It is interesting to note that while plastic shrinkage crack-

ing and evaporation are phenomena the concrete industry hastried to minimize as outlined in this paper, extensive work byJaegermann and Glucklich45 concluded that high evapora-tion soon after casting generally resulted in denser betterquality long-term concrete (albeit that some internal cracksexisted). They did indicate, however, that proper curingwould have to be provided.

CONCLUSIONS AND RECOMMENDATIONSPlastic shrinkage is normally associated with concrete slab

problems—primarily plastic shrinkage cracking.Researchers such as Menzel, Lerch, Bloem, Powers, and

others were instrumental in providing methods for predictingthe likelihood of plastic shrinkage cracking due to evapora-tion and concrete bleeding. The author has provided somefurther formulas, a simpler nomograph, and a set of guide-lines which should assist the cement and concrete industry inminimizing the onset of plastic shrinkage cracking.

The author believes that the “single figure” criterion fordeeming a critical evaporation rate needs to be addressed inlight of the factors outlined in this paper, in particular theconcrete strength (or w/c ratio) aspect.

While it is encouraging that researchers in the area of plas-tic shrinkage cracking seem to have adopted a standardmethod for testing slabs (i.e., the method proposed byKraai46 in 1985), the author feels that more research needs tobe carried out on thicker concrete specimens, i.e., more in-dicative of the typical slabs on building sites, e.g. 100 to 150mm (4 to 6 in.). In conjunction with this, the concretes usedin these tests should reflect the types of mixes that are be-coming more commonplace in the market, i.e., mixes con-taining water reducers, fly ash, slag, silica fume, plasticizers,and so on, thus gaining a better understanding of how the pa-rameters outlined in the latter part of this paper affect plasticshrinkage cracking.

CONVERSION FACTORS

1 m = 39.37 in.1 kph = 0.621 mph

1 kg = 2.204 lb1 kg/m2/hr = 0.205 lb/ft2 /hr

1 kPa = 0.145 psi

1 MJ = 947.8 BTU1 C = 5/9 (F – 32)

ACI Materials Journal / July-August 1998 375

REFERENCES1. ACI 305R-96. “Hot Weather Concreting.” Manual of Concrete Prac-

tice, Part 2. Farmington Hills: American Concrete Institute, 1996.2. Bloem, Delmar. “Plastic Cracking of Concrete.” Engineering Infor-

mation , National Ready Mixed Concrete Association/National Sand andGravel Association, July 1960, 2 p.

3. Lerch, William. “Plastic Shrinkage.” ACI Journal, Proceedings V. 53,No. 8, Feb. 1957, pp. 797-802.

4. “Prevention of Plastic Cracking in Concrete.” Concrete Information,Portland Cement Association, 1955.

5. Menzel, Carl A. “Causes and Prevention of Crack Development inPlastic Concrete.” Portland Cement Association Annual Meeting, 1954, pp.130-136.

6. Cebeci, O. Z., and Saatci, A. M. “Estimation of Evaporation fromConcrete Surfaces.” Concrete in Hot Climates, Proceedings , Third Interna-tional RILEM Conference, England, 1992, pp. 25-31.

7. Uno, P.; Kosmatka, S. H.; and Fiorato, A. Unpublished communica-tion, facsimile to Portland Cement Association, 1995.

8. Mather, Bryant, Discussion by Mather on paper by Zawde Berhane,“Evaporation of Water from Fresh Mortar and Concrete at Different Envi-ronmental Conditions,” ACI JOURNAL, Nov.-Dec. 1985, pp. 931-932.

9. Dalton, John. “Experimental Essays on Evaporation.” Manchester Lit.Phil. Soc. Mem. Proc., V. 5, 1802, pp. 536-602.

10. “Water Loss Investigations: Lake Hefner Studies, Technical Report.”Geological Survey Professional Paper 269, 1954 (originally. GeologicalSurvey Circular 229, 1952).

11. Kohler, M. A.; Nordenson, T. J.; and Fox, W. E., “Evaporation fromPans and Lakes,” Research Paper No. 38, U.S. Department of Commerce,Washington, May 1955.

12. Rohwer, Carl, “Evaporation from Free Water Surfaces.” TechnicalBulletin No. 271, United States Department of Agriculture, Washington,Dec. 1931.

13. Goff, J. A., and Gratch, S., “Low Pressure Properties of Water from160 to 212 F,” Trans. Am. Soc. Heat. Vent. Eng, V. 52, Paper 1286, 1946,pp. 95-122.

14. “Psychrometrics.” ASHRAE Handbook, 1993.15. Tetens, O., “Uber einige meteorologische Begriffe Z.,” Geophys. V.

6, 1930, pp. 297-309.16. Murray, F. W., “On the Computation of Saturation Vapor Pressure.”

J. Appl. Meteor., V. 6, Feb. 1967.17. Dilley, A. C., “On the Computer Calculation of Vapor Pressure and

Specific Humidity Gradients from Psychometric Data.” J. Appl. Meteor., V.7, Aug. 1968.

18. Mills, G. A., “A Comparison of Some Formulae for the Calculationof Saturation Vapor Pressure Over Water.” Meteorological Note No. 82,Bureau of Meteorology, Australia, Nov. 1975.

19. Observing the Weather, Australian Bureau of Meteorology, Dept. ofScience, 1991.

20. Linsley, Ray. K.; Kohler, Max. A.; and Paulhus, Joseph L. H.,Hydrology for Engineers, third ed., McGraw-Hill, 1988.

21. Veihmeyer, Frank J., “Evapotranspiration,” Handbook of AppliedHydrology, Ven Te Chow, editor, New York: McGraw-Hill, 1964.

22. Penman, H. L., “Natural Evaporation from Open Water, Bare Soil,and Grass,” Proc. R. Soc. London, Ser. A, 193, 1948, pp. 120-146.

23. Hasanain, G. S.; Khallaf, T. A.; and Mahmood, K., “Water Evapora-tion from Freshly Placed Concrete in Hot Weather.” Cement and ConcreteResearch, V. 19, 1989, pp. 465-475.

24. Ravina, Dan., and Shalon, Rahel, “Plastic Shrinkage Cracking.” ACIJOURNAL , Proceedings April 1968, pp. 282-291.

25. Van Dijk, J., and Boardman, V. R., “Plastic Shrinkage Cracking ofConcrete,” Proceedings, RILEM International Symposium on Concreteand Reinforced Concrete in Hot Countries, Technion, Israel Institute ofTechnology, Haifa, 1971, pp. 225-239.

26. CSA Standard A23.1 as referenced in Design and Control of Mixes,fifth Canadian Metric ed., Canadian Portland Cement Association, 1991.

27. “Cracks in Concrete Due to Plastic Shrinkage and Plastic Settle-

ment,” Technical Bulletin 95/1, Australian Pre-Mixed Concrete Associa-

tion, Oct. 1995.

28. “Plastic Cracking in Concrete,” Technical Information Letter No.

171-NRMCA, Modern Concrete, Oct. 1960, pp. 63-64.

29. Powers, Treval. C., “The Bleeding of Portland Cement Paste, Mortar

and Concrete,” Portland Cement Association Research Bulletin No. 2, June

1939.

30. Powers, Treval. C., The Properties of Fresh Concrete, John Wiley

and Sons, 1968.

31. Swayse, M. A., “Early Concrete Volume Changes and Their Con-

trol.” ACI JOU RNA L, Proceedings V. 38, 1942, pp. 425-440.

32. Wittman, F. H. “On the Action of Capillary Pressure in Fresh Con-

crete,” Cement and Concrete Research, V. 6, 1976, pp. 49-56.

33. Samman, T. A.; Mirza, W. H.; and Wafa, F. F., “Plastic Shrinkage

Cracking of Normal and High-Strength Concrete: A Comparative Study,”

ACI Materials Journal, V. 93, No. 1, Jan.-Feb. 1996, pp. 36-40.

34. Shaeles, Christos. A., and Hover, Kenneth C., “Influence of Mix Pro-

portions and Construction Operations on Plastic Shrinkage Cracking in

Thin Slabs,” ACI Materials Journal, V. 85, No. 6, Nov.-Dec. 1988, pp. 495-

504.

35. Schiessl, P., and Schmidt, R., “Bleeding of Concrete,” RILEM Pro-

ceedings of the Colloquium, Hanover, 1990, pp. 24-32.

36. Kral, S., and Gebauer, J., “Shrinkage and Cracking of Concrete at

Early Ages,” Proceedings , International Symposium on Slabs, Dundee,

1979; Advances in Concrete Slab Technology, London, Permagon Press,

1980, pp. 412-420.

37. Cabrera, J. G.; Cusens, A. R.; and Brookes-Wang, Y., “Effect of

Superplasticizers on the Plastic Shrinkage of Concrete,” Cement and Con-

crete Research, V. 44, No. 160, Sept. 1992, pp. 149-155.

38. Soroka, I., Concrete in Hot Environments , E & FN Spon, 1993.

39. Berke, N. S., and Dallaire, M. P., “The Effect of Low Addition Rates

of Polypropylene Fibers on Plastic Shrinkage Cracking and Mechanical

Properties of Concrete,” symposium abstract, SP-142. Detroit: American

Concrete Institute, 1993.

40. Balaguru, P., “Contribution of Fibers to Crack Reduction of Cement

Composites During the Initial and Final Setting Period,” ACI Materials

Journal, May-June 1994, pp. 280-288.

41. Campbell, Richard H.; Wendell, Harding; Misenhimer, Edward;

Nicholson, Leo P.; and Sisk, Jack, “Job Conditions Affect Cracking and

Strength of Concrete In-Place,” ACI JOURNAL, Proceedings Jan. 1976, pp.

10-13.

42. Turton, Colin D., Discussion on paper “Influence of Mix Proportions

and Construction Operations on Plastic Shrinkage Cracking in Thin Slabs,”

by Shaeles et al., ACI Materials Journal , Sep.-Oct. 1989, pp. 531-532.

43. Koberg, Gordon E.; Cruse, Robert R.; and Shrewsbury, Charles L.,

“Evaporation Control Research, 1959-60,” Geological Survey Water-Sup-

ply Paper 1692, U.S. Dept. of the Interior, pp. 1-53.

44. Cordon, William A., and Thorpe, J. Derle, “Control of Rapid Drying

of Fresh Concrete by Evaporation Control,” ACI JO URN AL, Proceedings

Aug. 1965, pp. 977-984.

45. Jaegermann, C. H., and Glucklich, J., “Effect of Exposure of Fresh

Concrete to High Evaporation and Elevated Temperatures on the Long-

Time Properties of Hardened Concrete.” Proceedings , RILEM Sympo-

sium, Israel, V. 1, Aug. 1971, pp. 383-422.

46. Kraai, P. O., “Proposed Test to Determine the Cracking Potential

Due to Drying Shrinkage of Concrete,” Concrete Construction, Sept. 1985,

pp. 775-778.